paper

Local Whittle estimation in nonstationary and unit root cases

arXiv:math/0406462 · doi:10.1214/009053604000000139

Abstract

Asymptotic properties of the local Whittle estimator in the nonstationary case (d>{1/2}) are explored. For {1/2}<d\leq 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d=1, the limit distribution is mixed normal. For d>1 and when the process has a polynomial trend of order α>{1/2}, the estimator is shown to be inconsistent and to converge in probability to unity.

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